Problem: Solve for $x$ and $y$ using elimination. ${5x-2y = -8}$ ${6x+2y = 30}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2y$ and $2y$ cancel out. $11x = 22$ $\dfrac{11x}{{11}} = \dfrac{22}{{11}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {5x-2y = -8}\thinspace$ to find $y$ ${5}{(2)}{ - 2y = -8}$ $10-2y = -8$ $10{-10} - 2y = -8{-10}$ $-2y = -18$ $\dfrac{-2y}{{-2}} = \dfrac{-18}{{-2}}$ ${y = 9}$ You can also plug ${x = 2}$ into $\thinspace {6x+2y = 30}\thinspace$ and get the same answer for $y$ : ${6}{(2)}{ + 2y = 30}$ ${y = 9}$